The Erdős–Moser equation is a specific type of functional equation that arises in the context of additive combinatorics and related fields in mathematics. The equation is named after Paul Erdős and Leo Moser, who studied its properties.

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The Erdős–Straus conjecture is a problem in number theory that was proposed by the mathematicians Paul Erdős and George Strauss in 1948. The conjecture asserts that for every integer \( n \geq 2 \), the equation \[ \frac{4}{n} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \] has solutions in positive integers \( x, y, z \).

An Euler brick is a special type of rectangular cuboid (or box) with integer side lengths \(a\), \(b\), and \(c\) such that the lengths of the three face diagonals are also integers. Specifically, the conditions for an Euler brick are that: 1. The dimensions are positive integers: \(a\), \(b\), and \(c\). 2. The lengths of the face diagonals are also integers.

Fermat's right triangle theorem states that if \( a \), \( b \), and \( c \) are the lengths of the sides of a right triangle, with \( c \) being the length of the hypotenuse, then the only integer solutions to the equation \( a^2 + b^2 = c^2 \) occur for certain sets of values for \( a \), \( b \), and \( c \).

The Goormaghtigh conjecture is a hypothesis in the field of number theory, specifically concerning the distribution of prime numbers and their relationship with integers. Proposed by the Belgian mathematician Louis Goormaghtigh in the early 20th century, the conjecture states that there are infinitely many prime numbers \( p \) such that \( p + 1 \) is a perfect square.

Hilbert's tenth problem, proposed by mathematician David Hilbert in 1900, asks for an algorithm that, given a polynomial Diophantine equation—a polynomial equation where the variables are to be integers—will determine whether there are any integer solutions to that equation.

Hippolyte Sébron (1821–1879) was a French painter known for his contributions to the art world during the 19th century. He was primarily associated with the realist movement and is often recognized for his detailed and vibrant landscape paintings, as well as portraits and historical scenes. Sébron was influenced by the naturalistic approach of his contemporaries, and his works often capture the essence of French rural life and the beauty of the countryside.

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The Jacobi–Madden equation refers to a mathematical relationship that arises in the context of dynamics, particularly in the study of second-order equations and Hamiltonian mechanics. It is associated with the properties and transformations of certain integrable systems.

The Lander, Parkin, and Selfridge conjecture is a statement in number theory that pertains to the existence of certain types of prime numbers. Specifically, it deals with prime numbers that can be represented in a specific way using two distinct primes.

Legendre's equation, often encountered in mathematical physics and potential theory, refers to a specific type of ordinary differential equation. It is given in the context of Legendre polynomials, which are solutions to this equation.

Leonid Levin is a prominent computer scientist known for his significant contributions to computational complexity theory, algorithms, and computer science in general. He was born in 1948 in the former Soviet Union and later emigrated to the United States. Levin is particularly known for his work on NP-completeness and for his contributions to the theory of randomized algorithms.

A Markov number is a specific type of positive integer that is associated with a particular solution to Markov's equation, which is given by: \[ x^2 + y^2 + z^2 = 3xyz \] where \( x \), \( y \), and \( z \) are positive integers. A set of numbers \( (x, y, z) \) that satisfies this equation is called a Markov triple.

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The Banach-Mazur game is a two-player game in the field of set theory and topology, particularly in the context of functional analysis. It is named after mathematicians Stefan Banach and Juliusz Mazur, who introduced the game in the early 20th century. ### Rules of the Game: 1. **Players**: There are two players, typically called Player I and Player II.

The history of web browsers is a fascinating journey through the evolution of the internet, starting from its early days in the late 1980s to the highly advanced browsers we use today. Here’s an overview of key milestones in the development of web browsers: ### 1. **The Early Days (1980s)** - **1989 – Tim Berners-Lee**: The World Wide Web was proposed by Tim Berners-Lee, who worked at CERN.

An algebraic differential equation is a type of differential equation that involves algebraic expressions in the unknown function and its derivatives, but does not involve any transcendental functions like exponentials, logarithms, or trigonometric functions. Essentially, it is a differential equation where the relationship between the function and its derivatives can be expressed entirely in terms of polynomials or rational functions.